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Title: Adiabatic theorem for non-Hermitian time-dependent open systems

Abstract

In the conventional quantum mechanics (i.e., Hermitian quantum mechanics) the adiabatic theorem for systems subjected to time-periodic fields holds only for bound systems and not for open ones (where ionization and dissociation take place) [D. W. Hone, R. Ketzmerik, and W. Kohn, Phys. Rev. A 56, 4045 (1997)]. Here with the help of the (t,t{sup '}) formalism combined with the complex scaling method we derive an adiabatic theorem for open systems and provide an analytical criterion for the validity of the adiabatic limit. The use of the complex scaling transformation plays a key role in our derivation. As a numerical example we apply the adiabatic theorem we derived to a one-dimensional model Hamiltonian of Xe atom which interacts with strong, monochromatic sine-square laser pulses. We show that the generation of odd-order harmonics and the absence of hyper-Raman lines, even when the pulses are extremely short, can be explained with the help of the adiabatic theorem we derived.

Authors:
;  [1]
  1. Department of Chemistry and Minerva Center of Nonlinear Physics in Complex Systems Technion, Israel Institute of Technology, Haifa 32000 (Israel)
Publication Date:
OSTI Identifier:
20718476
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 72; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.72.032103; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; DISSOCIATION; HAMILTONIANS; HARMONIC GENERATION; HARMONICS; IONIZATION; LASER RADIATION; MONOCHROMATIC RADIATION; ONE-DIMENSIONAL CALCULATIONS; OPTICS; PERIODICITY; PHOTON-ATOM COLLISIONS; PULSES; QUANTUM MECHANICS; TIME DEPENDENCE; TRANSFORMATIONS; XENON

Citation Formats

Fleischer, Avner, and Moiseyev, Nimrod. Adiabatic theorem for non-Hermitian time-dependent open systems. United States: N. p., 2005. Web. doi:10.1103/PhysRevA.72.032103.
Fleischer, Avner, & Moiseyev, Nimrod. Adiabatic theorem for non-Hermitian time-dependent open systems. United States. https://doi.org/10.1103/PhysRevA.72.032103
Fleischer, Avner, and Moiseyev, Nimrod. 2005. "Adiabatic theorem for non-Hermitian time-dependent open systems". United States. https://doi.org/10.1103/PhysRevA.72.032103.
@article{osti_20718476,
title = {Adiabatic theorem for non-Hermitian time-dependent open systems},
author = {Fleischer, Avner and Moiseyev, Nimrod},
abstractNote = {In the conventional quantum mechanics (i.e., Hermitian quantum mechanics) the adiabatic theorem for systems subjected to time-periodic fields holds only for bound systems and not for open ones (where ionization and dissociation take place) [D. W. Hone, R. Ketzmerik, and W. Kohn, Phys. Rev. A 56, 4045 (1997)]. Here with the help of the (t,t{sup '}) formalism combined with the complex scaling method we derive an adiabatic theorem for open systems and provide an analytical criterion for the validity of the adiabatic limit. The use of the complex scaling transformation plays a key role in our derivation. As a numerical example we apply the adiabatic theorem we derived to a one-dimensional model Hamiltonian of Xe atom which interacts with strong, monochromatic sine-square laser pulses. We show that the generation of odd-order harmonics and the absence of hyper-Raman lines, even when the pulses are extremely short, can be explained with the help of the adiabatic theorem we derived.},
doi = {10.1103/PhysRevA.72.032103},
url = {https://www.osti.gov/biblio/20718476}, journal = {Physical Review. A},
issn = {1050-2947},
number = 3,
volume = 72,
place = {United States},
year = {Thu Sep 15 00:00:00 EDT 2005},
month = {Thu Sep 15 00:00:00 EDT 2005}
}